English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

If P is any point in the interior of a parallelogram ABCD, then prove that area of the
triangle APB is less than half the area of parallelogram.

If AD is a median of a triangle ABC, then prove that triangles ADB and ADC are equal in
area. If G is the mid-point of median AD, prove that ar (Δ BGC) = 2 ar (Δ AGC).

A point D is taken on the side BC of a ΔABC such that BD = 2DC. Prove that ar(Δ ABD) =
2ar (ΔADC).

ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove
that:  (1) ar (ΔADO) = ar (ΔCDO)     (2) ar (ΔABP) = ar (ΔCBP)

ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects
CD at F.
(i) Prove that ar (ΔADF) = ar (ΔECF)
(ii) If the area of ΔDFB = 3 cm2, find the area of ||^gm ABCD.

ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O
intersects AB at P and DC at Q. Prove that ar (Δ POA) = ar (Δ QOC).

ABCD is a parallelogram. E is a point on BA such that BE = 2 EA and F is a point on DC
such that DF = 2 FC. Prove that AE CF is a parallelogram whose area is one third of the
area of parallelogram ABCD.

Prove that two different circles cannot intersect each other at more than two points.

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Suppose You Are Given a Circle. Give a Construction to Find Its Centre.

In below fig., PSDA is a parallelogram in which PQ = QR = RS and AP || BQ || CR. Prove
that ar (Δ PQE) = ar (ΔCFD).

In the below fig. O is the centre of the circle. If ∠APB = 50°, find ∠AOB and ∠OAB.

In the fig below, it is given that O is the centre of the circle and ∠AOC = 150°. Find
∠ABC.

D is the mid-point of side BC of ΔABC and E is the mid-point of BD. if O is the mid-point
of AE, prove that ar (ΔBOE) = `1/8` ar (Δ ABC).

In the below fig. X and Y are the mid-points of AC and AB respectively, QP || BC and
CYQ and BXP are straight lines. Prove that ar (Δ ABP) = ar (ΔACQ).

In Fig. 10.25, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD. 

Determine the measure of each of the equal angles of a right-angled isosceles triangle.  

OR
ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

AB is a line segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB. 

Draw a line segment of length 8.6 cm. Bisect it and measure the length of each part.

What do you understand by the word “statistics” in
(i) Singular form
(ii) Plural form?